Abstract

The objective of this paper is to present an inequality decomposition method, the two-stage nested Theil decomposition method, which is an extension of the ordinary one-stage Theil decomposition method. The method is analogous to a two-stage nested design in the analysis of variance (ANOVA). It considers the three-level hierarchical structure of a country: region-province-district, and decomposes the overall regional inequality, as measured by Theil indices based on district-level mean incomes, into three components: the between-region, between-province, and within-province inequality components. The within-province component is a weighted-average of within-province income inequalities for each province, while the between-province component is a weighted-average of between-province income inequalities within each region. The method uses districts as a basic regional unit to measure regional income inequality, rather than provinces, and thus can analyze the contribution of within-province inequalities as well as between-province and between-region inequalities to the overall regional income inequality in a coherent framework. This paper applies this two-stage nested Theil decomposition method to district-level income and population data in China and Indonesia and explores the factors of regional income inequality in China and Indonesia.